In the case of \(1-4\)  moves, one can apply the same method on \({\bf T}_4\) , resulting in a divergent term \(\delta _{\mathrm {SU}(2)}(\mathbb {I})\) .
Indeed, the holonomies surrounding the four edges incident to the internal vertex are on four loops patched together to form a 2-sphere. Thus only three of the four delta functions of these holonomies are independent, which gives one extra delta function evaluated on identity.
This divergence corresponds to the translational symmetry of the internal vertex of \({\bf T}_4\) , which is the infinite gauge volume of the Lie algebra \({\mathfrak {su}}(2)\)  [1]}, [2]}.
To remove the divergence, one can go through the partial gauge fixing method [3]} (or equivalently the Fadeev-Popov gauge fixing procedure illustrated in [1]}, [5]}).
